he area enclosed between the curves y=ax2  and x=ay2(a>0)𝑦=𝑎𝑥2  and 𝑥=𝑎𝑦2(𝑎>0) is 11 square unit, then the value of a𝑎 is:

To find the value of 'a', we first need to find the points of intersection of the two curves y=ax^2 and x=ay^2.

Step 1: Set the two equations equal to each other:

ax^2 = ay^2

Step 2: Simplify the equation:

x^2 = y^2

Step 3: Solve for y:

y = ±x

The curves intersect at the points where y = x and y = -x.

Next, we need to find the area between the curves. The area between two curves is given by the integral of the absolute difference of the functions.

Step 4: Set up the integral:

Area = ∫ from -1 to 1 (ax^2 - ax^2) dx

Step 5: Simplify the integral:

Area = ∫ from -1 to 1 (0) dx = 0

However, we are given that the area is 1 square unit. This is a contradiction, which suggests that there may be a mistake in the problem statement. The area between the curves y=ax^2 and x=ay^2 cannot be 1 square unit for any value of 'a'.